Chapter Eleven: Rate and Mass of Surplus Value

In this chapter, as hitherto, the value of labour-power,
and therefore the part of the working day necessary for the reproduction
or maintenance of that labour-power, are supposed to be given, constant
magnitudes.

This premised, with the rate, the mass is at the same time given
of the surplus-value that the individual labourer furnishes to the capitalist
in a definite period of time. If, e.g., the necessary labour amounts
to 6 hours daily, expressed in a quantum of gold = 3 shillings, then 3s.
is the daily value of one labour-power or the value of the capital advanced
in the buying of one labour-power. If, further, the rate of surplus-value
be = 100%, this variable capital of 3s. produces a mass of surplus-value
of 3s., or the labourer supplies daily a mass of surplus labour equal to
6 hours.

But the variable capital of a capitalist is the expression in
money of the total value of all the labour-powers that he employs simultaneously.
Its value is, therefore, equal to the average value of one labour-power,
multiplied by the number of labour-powers employed. With a given value
of labour-power, therefore, the magnitude of the variable capital varies
directly as the number of labourers employed simultaneously. If the daily
value of one labour-power = 3s., then a capital of 300s. must be advanced
in order to exploit daily 100 labour-powers, of n times 3s., in order to
exploit daily n labour-powers.

In the same way, if a variable capital of 3s., being the daily
value of one labour-power, produce a daily surplus-value of 3s., a variable
capital of 300s. will produce a daily surplus-value of 300s., and one of
n times 3s. a daily surplus-value of n × 3s. The mass of the surplus-value
produced is therefore equal to the surplus-value which the working day of
one labourer supplies multiplied by the number of labourers employed. But
as further the mass of surplus-value which a single labourer produces, the
value of labour-power being given, is determined by the rate of the surplus-value,
this law follows: the mass of the surplus-value produced is equal
to the amount of the variable capital advanced, multiplied by the rate
of surplus-value, in other words: it is determined by the compound ratio
between the number of labour-powers exploited simultaneously by the same
capitalist and the degree of exploitation of each individual labour-power.

Let the mass of the surplus-value be S, the surplus-value supplied
by the individual labourer in the average day s the variable capital daily
advanced in the purchase of one individual labour-power v, the sum total
of the variable capital V, the value of an average labour-power P, its
degree of exploitation (a'/a) (surplus-labour/necessary-labour) and the number of labourers employed n; we have:

S =

{

(s/v) × V

P × (a'/a) × n

It is always supposed, not only that the value of an average labour-power
is constant, but that the labourers employed by a capitalist are reduced
to average labourers. There are exceptional cases in which the surplus-value
produced does not increase in proportion to the number of labourers exploited,
but then the value of the labour-power does not remain constant.

In the production of a definite mass of surplus-value, therefore
the decrease of one factor may be compensated by the increase of the other.
If the variable capital diminishes, and at the same time the rate of surplus-value
increases in the same ratio, the mass of surplus-value produced remains
unaltered. If on our earlier assumption the capitalist must advance 300s.,
in order to exploit 100 labourers a day, and if the rate of surplus-value
amounts to 50%, this variable capital of 300s. yields a surplus-value of
150s. or of 100 × 3 workinghours. If the rate of surplus-value doubles,
or the working day, instead of being extended from 6 to 9, is extended from
6 to 12 hours and at the same time variable capital is lessened by half,
and reduced to 150s., it yields also a surplus-value of 150s. or 50 × 6
workinghours. Diminution of the variable capital may therefore be compensated
by a proportionate rise in the degree of exploitation of labour-power,
or the decrease in the number of the labourers employed by a proportionate
extension of the working day. Within certain limits therefore the supply
of labour exploitable by capital is independent of the supply of labourers.
[1] On the contrary, a fall in the rate of surplus-value leaves unaltered the mass of the surplus-value produced, if the amount
of the variable capital, or number of the labourers employed, increases
in the same proportion.

Nevertheless, the compensation of a decrease in the number of
labourers employed, or of the amount of variable capital advanced by a
rise in the rate of surplus-value, or by the lengthening of the working-day,
has impassable limits. Whatever the value of labour-power may be, whether
the workingtime necessary for the maintenance of the labourer is 2 or 10
hours, the total value that a labourer can produce, day in, day out, is
always less than the value in which 24 hours of labour are embodied, less
than 12s., if 12s. is the money expression for 24 hours of realised labour.
In our former assumption, according to which 6 workinghours are daily necessary
in order to reproduce the labour-power itself or to replace the value of
the capital advanced in its purchase, a variable capital of 1,500s., that
employs 500 labourers at a rate of surplus-value of 100% with a 12 hours’
working day, produces daily a surplus-value of 1,500s. or of 6 × 500 workinghours.
A capital of 300s. that employs 100 labourers a day with a rate of surplus-value
of 200% or with a working day of 18 hours, produces only a mass of surplus-value
of 600s. or 12 × 100 workinghours; and its total value-product, the equivalent
of the variable capital advanced plus the surplus-value, can, day in, day
out, never reach the sum of 1,200s. or 24 × 100 workinghours. The absolute
limit of the average working day — this being by nature always less than
24 hours — sets an absolute limit to the compensation of a reduction of
variable capital by a higher rate of surplus-value, or of the decrease of
the number of labourers exploited by a higher degree of exploitation of
labour-power. This palpable law is of importance for the clearing up of
many phenomena, arising from a tendency (to be worked out later on) of
capital to reduce as much as possible the number of labourers employed
by it, or its variable constituent transformed into labour-power, in contradiction
to its other tendency to produce the greatest possible mass of surplus-value.
On the other hand, if the mass of labour-power employed, or the amount
of variable capital, increases, but not in proportion to the fall in the
rate of surplus-value, the mass of the surplus-value produced, falls.

A third law results from the determination, of the mass of the
surplus-value produced, by the two factors: rate of surplus-value and amount
of variable capital advanced. The rate of surplus-value, or the degree of
exploitation of labour-power, and the value of labour-power, or the amount
of necessary workingtime being given, it is selfevident that the greater
the variable capital, the greater would be the mass of the value produced
and of the surplus-value. If the limit of the working-day is given, and
also the limit of its necessary constituent, the mass of value
and surplus-value that an individual capitalist produces, is clearly exclusively
dependent on the mass of labour that he sets in motion. But this, under
the conditions supposed above, depends on the mass of labour-power, or
the number of labourers whom he exploits, and this number in its turn is
determined by the amount of the variable capital advanced. With a given
rate of surplus-value, and a given value of labour-power, therefore, the
masses of surplus-value produced vary directly as the amounts of the variable
capitals advanced. Now we know that the capitalist divides his capital
into two parts. One part he lays out in means of production. This is the
constant part of his capital. The other part he lays out in living labour-power.
This part forms his variable capital. On the basis of the same mode of
social production, the division of capital into constant and variable differs
in different branches of production, and within the same branch of production,
too, this relation changes with changes in the technical conditions and
in the social combinations of the processes of production. But in whatever
proportion a given capital breaks up into a constant and a variable part,
whether the latter is to the former as 1:2 or 1:10 or 1:x, the law just
laid down is not affected by this. For, according to our previous analysis,
the value of the constant capital reappears in the value of the product,
but does not enter into the newly produced value, the newly created value product.
To employ 1,000 spinners, more raw material, spindles, &c., are, of
course, required, than to employ 100. The value of these additional means
of production however may rise, fall, remain unaltered, be large or small;
it has no influence on the process of creation of surplus-value by means
of the labour-powers that put them in motion. The law demonstrated above
now, therefore, takes this form: the masses of value and of surplus-value
produced by different capitals — the value of labour-power being given
and its degree of exploitation being equal — vary directly as the amounts
of the variable constituents of these capitals, i.e., as their constituents
transformed into living labour-power.

This law clearly contradicts all experience based on appearance.
Everyone knows that a cotton spinner, who, reckoning the percentage on
the whole of his applied capital, employs much constant and little variable
capital, does not, on account of this, pocket less profit or surplus-value
than a baker, who relatively sets in motion much variable and little constant
capital. For the solution of this apparent contradiction, many intermediate
terms are as yet wanted, as from the standpoint of elementary algebra many
intermediate terms are wanted to understand that 0/0 may represent an actual
magnitude. Classical economy, although not formulating the law, holds instinctively
to it, because it is a necessary consequence of the general law of value.
It tries to rescue the law from collision with contradictory
phenomena by a violent abstraction. It will be seen later[2] how the school of Ricardo has come to grief over this stumbling block. Vulgar economy which, indeed, “has really learnt nothing,” here as everywhere
sticks to appearances in opposition to the law which regulates and explains
them. In opposition to Spinoza, it believes that “ignorance is a sufficient
reason.”

The labour which is set in motion by the total capital of a society,
day in, day out, may be regarded as a single collective working day. If,
e.g., the number of labourers is a million, and the average working-day
of a labourer is 10 hours, the social working day consists of ten million
hours. With a given length of this working day, whether its limits are fixed
physically or socially, the mass of surplus-value can only be increased
by increasing the number of labourers, i.e., of the labouring population.
The growth of population here forms the mathematical limit to the production
of surplus-value by the total social capital. On the contrary, with a given
amount of population, this limit is formed by the possible lengthening
of the working day.[3] It will, however, be seen in the following chapter that this law only holds for the form of surplus-value dealt with up to the present.

From the treatment of the production of surplus-value, so far,
it follows that not every sum of money, or of value, is at pleasure transformable
into capital. To effect this transformation, in fact, a certain minimum
of money or of exchange-value must be presupposed in the hands of the individual
possessor of money or commodities. The minimum of variable capital is the
cost price of a single labour-power, employed the whole year through, day
in, day out, for the production of surplus-value. If this labourer were
in possession of his own means of production, and were satisfied to live
as a labourer, he need not work beyond the time necessary for the reproduction
of his means of subsistence, say 8 hours a day. He would, besides, only
require the means of production sufficient for 8 working-hours. The capitalist,
on the other hand, who makes him do, besides these 8 hours, say 4 hours’
surplus-labour, requires an additional sum of money for furnishing the
additional means of production. On our supposition, however, he would have
to employ two labourers in order to live, on the surplus-value appropriated
daily, as well as, and no better than a labourer, i.e., to be able to satisfy
his necessary wants. In this case the mere maintenance of life would be
the end of his production, not the increase of wealth; but this latter
is implied in capitalist production. That he may live only twice as well as an ordinary labourer, and besides turn half of the surplus-value produced
into capital, he would have to raise, with the number of labourers, the
minimum of the capital advanced 8 times. Of course he can, like his labourer,
take to work himself, participate directly in the process of production,
but he is then only a hybrid between capitalist and labourer, a “small
master.” A certain stage of capitalist production necessitates that the
capitalist be able to devote the whole of the time during which he functions
as a capitalist, i.e., as personified capital, to the appropriation
and therefore control of the labour of others, and to the selling of the
products of this labour.[4] The guilds of the middle
ages therefore tried to prevent by force the transformation of the master
of a trade into a capitalist, by limiting the number of labourers that
could be employed by one master within a very small maximum. The possessor
of money or commodities actually turns into a capitalist in such cases
only where the minimum sum advanced for production greatly exceeds the
maximum of the middle ages. Here, as in natural science, is shown the correctness
of the law discovered by Hegel (in his “Logic”), that merely quantitative
differences beyond a certain point pass into qualitative changes.[5]

The minimum of the sum of value that the individual possessor
of money or commodities must command, in order to metamorphose himself
into a capitalist, changes with the different stages of development of
capitalist production, and is at given stages different in different spheres
of production, according to their special and technical conditions. Certain
spheres of production demand, even at the very outset of capitalist production,
a minimum of capital that is not as yet found in the hands of single individuals.
This gives rise partly to state subsidies to private persons, as in France
in the time of Clobber, and as in many German states up to our own epoch,
partly to the formation of societies with legal monopoly for the exploitation
of certain branches of industry and commerce, the forerunners of our modern
joint stock companies.[6]

Within the process of production, as we have seen, capital acquired
the command over labour, i.e., over functioning labour-power or
the labourer himself. Personified capital, the capitalist takes care that
the labourer does his work regularly and with the proper degree of intensity.

Capital further developed into a coercive relation, which compels
the working class to do more work than the narrow round of its own life-wants
prescribes. As a producer of the activity of others, as a pumper-out of
surplus labour and exploiter of labour-power, it surpasses in energy, disregard
of bounds, recklessness and efficiency, all earlier systems of production
based on directly compulsory labour.

At first, capital subordinates labour on the basis of the technical
conditions in which it historically finds it. It does not, therefore, change
immediately the mode of production. The production of surplus-value — in
the form hitherto considered by us — by means of simple extension of the
working day, proved, therefore, to be independent of any change in the mode
of production itself. It was not less active in the old-fashioned bakeries
than in the modern cotton factories.

If we consider the process of production from the point of view
of the simple labour process, the labourer stands in relation to the means
of production, not in their quality as capital, but as the mere means and
material of his own intelligent productive activity. In tanning, e.g.,
he deals with the skins as his simple object of labour. It is not the capitalist
whose skin he tans. But it is different as soon as we deal with the process
of production from the point of view of the process of creation of surplus-value.
The means of production are at once changed into means for the absorption
of the labour of others. It is now no longer the labourer that employs
the means of production, but the means of production that employ
the labourer. Instead of being consumed by him as material elements of
his productive activity, they consume him as the ferment necessary to their
own life-process, and the life-process of capital consists only in its movement
as value constantly expanding, constantly multiplying itself. Furnaces
and workshops that stand idle by night, and absorb no living labour, are
“a mere loss” to the capitalist. Hence, furnaces and workshops constitute
lawful claims upon the night-labour of the work-people. The simple transformation
of money into the material factors of the process of production, into means
of production, transforms the latter into a title and a right to the labour
and surpluslabour of others. An example will show, in conclusion, how this
sophistication, peculiar to and characteristic of capitalist production,
this complete inversion of the relation between dead and living labour,
between value and the force that creates value, mirrors itself in the consciousness
of capitalists. During the revolt of the English factory lords between
1848 and 1850, “the head of one of the oldest and most respectable houses
in the West of Scotland, Messrs. Carlile Sons & Co., of the linen and
cotton thread factory at Paisley, a company which has now existed for about
a century, which was in operation in 1752, and four generations of the
same family have conducted it” ... this “very intelligent gentleman” then
wrote a letter[7] in the Glasgow Daily Mail of April 25th, 1849, with the title, “The relay system,” in which among other
things the following grotesquely naïve passage occurs: “Let us now
... see what evils will attend the limiting to 10 hours the working of
the factory.... They amount to the most serious damage to the millowner’s
prospects and property. If he (i.e., his “hands”) worked 12 hours before, and
is limited to 10, then every 12 machines or spindles in his establishment
shrink to 10, and should the works be disposed of, they will be valued
only as 10, so that a sixth part would thus be deducted from the value
of every factory in the country.”[8]

To this West of Scotland bourgeois brain, inheriting the accumulated
capitalistic qualities of “four generations,” the value of the means of
production, spindles, &c., is so inseparably mixed up with their property,
as capital, to expand their own value, and to swallow up daily a
definite quantity of the unpaid labour of others, that the head of the
firm of Carlile & Co. actually imagines that if he sells his factory,
not only will the value of the spindles be paid to him, but, in addition,
their power of annexing surplus-value, not only the labour which is embodied
in them, and is necessary to the production of spindles of this kind, but
also the surpluslabour which they help to pump out daily from the brave
Scots of Paisley, and for that very reason he thinks that with the shortening
of the working day by 2 hours, the selling-price of 12 spinning machines
dwindles to that of 10!

Footnotes

1. This elementary law appears to be unknown to the vulgar economists, who, upside-down Archimedes, in the determination
of the market-price of labour by supply and demand, imagine they have found the fulcrum by means of which, not to move the world, but to stop its motion.

3. “The Labour, that is the economic time, of society, is a given portion, say ten hours a day of a million of people, or ten million hours.... Capital has its boundary of increase. This boundary may, at any given period, be attained in the actual extent of economic time employed.” (“An Essay on the Political Economy of Nations.” London, 1821, pp. 47, 49.)

4. “The farmer cannot rely on his own labour, and if he does, I will maintain that he is a loser by it. His employment
should be a general attention to the whole: his thresher must be watched,
or he will soon lose his wages in corn not threshed out, his mowers, reapers,
&c., must be looked after; he must constantly go round his fences;
he must see there is no neglect; which would be the case if he was confined
to any one spot.” (“An Inquiry into the Connexion between the Present
Price of Provisions and the Size of Farms, &c. By a Farmer.” London,
1773, p. 12.) This book is very interesting. In it the genesis of the “capitalist
farmer” or “merchant farmer,” as he is explicitly called, may be studied,
and his self-glorification at the expense of the small farmer who has only
to do with bare subsistence, be noted. “The class of capitalists are from
the first partially, and they become ultimately completely, discharged
from the necessity of the manual labour.” (“Textbook of Lectures on the
Political Economy of Nations. By the Rev. Richard Jones.” Hertford 1852.
Lecture III., p. 39.)

5. The molecular theory of modern chemistry first scientifically worked out by Laurent and Gerhardt rests on no other law. (Addition to 3rd Edition.) For the explanation of this statement, which is not very clear to non-chemists, we remark that the author speaks here of the homologous series of carbon compounds, first so named by C. Gerhardt in 1843, each series of which has its own general algebraic formula.
Thus the series of paraffins: CnH2n+2, that of the normal alcohols: CnH2n+2O;
of the normal fatty acids: CnH2nO2 and many others. In the above examples, by the simply quantitative addition of CH2 to the molecular formula, a qualitatively different body is each time formed. On the share (overestimated
by Marx) of Laurent and Gerhardt in the determination of this important fact see Kopp, “Entwicklung der Chemie.” Munchen, 1873, pp. 709, 716, and Schorkmmer, “The Rise and Development of Organic Chemistry.” London, 1879, p. 54. — F. E.. See Letter from Marx to Engels, 22 June 1867

8. l.c., p. 60. Factory Inspector Stuart, himself a Scotchman, and in contrast to the English Factory Inspectors,
quite taken captive by the capitalistic method of thinking, remarks expressly
on this letter which he incorporates in his report that it is “the most
useful of the communications which any of the factory-owners working with
relays have given to those engaged in the same trade, and which is the
most calculated to remove the prejudices of such of them as have scruples
respecting any change of the arrangement of the hours of work.”